GenoDRPh
GenoDRPh
Joined: Aug 4, 2022
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Dieter
August 4th, 2022 at 12:52:39 PM permalink
Hello All,

Longtime lurker, first time poster. My local pub, that I used to frequent before the pandemic hit, has a dice game. $1 to play, which goes in to the pot. You roll 5 standard 6 sided dice. A three of a kind of any number gets you a free roll. Four a kind of any number gets you $100 from the pot. Five of a kind gets you the whole pot, minus 15% tip to the bartender(s) on duty at that particular time. I someone willing to do a statistical analysis of the game here. such as house edge, break even, etc? My statistics background is in clinical trials and medical studies and experiments, and not in gambling at all. Thanks for your assistance.

Gene
Dieter
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Dieter
Joined: Jul 23, 2014
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August 4th, 2022 at 1:45:56 PM permalink
I know some bar dice variants allow partial rerolls, like yahtzee.
Is that allowed, so you can hold a pair, and reroll the other 3 dice?

You say a 3 of a kind gets a "free roll".
Does that mean you roll all 5 dice again?
May the cards fall in your favor.
camapl
camapl
Joined: Jun 22, 2010
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August 4th, 2022 at 2:18:49 PM permalink
Good questions, Dieter!

Also, is any money added to the pot after it hits, or does it start from zero? What happens when someone rolls a four of a kind with less than $100 in the pot (think multiple hits in short succession)?
* Actual results may vary.
gordonm888
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gordonm888
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August 4th, 2022 at 2:39:20 PM permalink
Quote: GenoDRPh

Hello All,

Longtime lurker, first time poster. My local pub, that I used to frequent before the pandemic hit, has a dice game. $1 to play, which goes in to the pot. You roll 5 standard 6 sided dice. A three of a kind of any number gets you a free roll. Four a kind of any number gets you $100 from the pot. Five of a kind gets you the whole pot, minus 15% tip to the bartender(s) on duty at that particular time. I someone willing to do a statistical analysis of the game here. such as house edge, break even, etc? My statistics background is in clinical trials and medical studies and experiments, and not in gambling at all. Thanks for your assistance.

Gene
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Welcome to the forum! It's always good to take a peek at the forum rules: Forum Rules.

The analysis you are asking for is straightforward and relatively easy. I'm busy and can't do it right now, but I'm sure someone will step up shortly.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
GenoDRPh
GenoDRPh
Joined: Aug 4, 2022
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August 4th, 2022 at 3:12:14 PM permalink
Thanks everyone for your responses. I may have left out some crucial information, which I realize after reading my original post. A free roll means you can roll all five dice again, but you must roll all 5 dice. All wagers go in to the pot, which increases with each bet-so I guess you can call that progressive. There's no rake to the house with each bet, other than the 15% to the bartender(s) on duty on a 5 of a kind. As an aside, I've never seen anyone other than one or both of the two ladies who own the place work behind the bar, so maybe you can call that a rake of a sort. I don't know where the seed money for pot comes from, but let's assume that the house puts up a few bucks-let's say to always keep the pot at $200 minimum. I've never been in there when someone's won anything, and have seen the pot in the thousands. Someone did win a bit over $5k once, but I wasn't there, do not know how long the game went without a jackpot winner and the next time I went in the jackpot was a bit over $900.

Gene
Dieter
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Dieter
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August 4th, 2022 at 4:21:57 PM permalink
Assuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.
May the cards fall in your favor.
unJon
unJon
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August 4th, 2022 at 7:17:29 PM permalink
Quote: Dieter

Assuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.
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Itís lower. $1525 ignores the 4 of a kind payout and 3 of a kind re-roll.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Dieter
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Dieter
Joined: Jul 23, 2014
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August 4th, 2022 at 7:25:55 PM permalink
Quote: unJon

Quote: Dieter

Assuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.
link to original post



Itís lower. $1525 ignores the 4 of a kind payout and 3 of a kind re-roll.
link to original post



... and as soon as someone hits the 4oK for $100, the pot shrinks, making the game undesirable.

Lots of fun math here for someone smarter than me to grind on.
May the cards fall in your favor.
unJon
unJon
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August 4th, 2022 at 7:44:19 PM permalink
Quote: Dieter

Quote: unJon

Quote: Dieter

Assuming that any 5 of a kind is good for a win, my sloppy math says it's positive at $1525 in the pot.

The actual number is probably lower, and I'm happy to hear why.
link to original post



Itís lower. $1525 ignores the 4 of a kind payout and 3 of a kind re-roll.
link to original post



... and as soon as someone hits the 4oK for $100, the pot shrinks, making the game undesirable.

Lots of fun math here for someone smarter than me to grind on.
link to original post



I donít follow that comment. You know the prize pool when you roll. One person rolls at a time.

6^5 = 7,776 ways to roll 5 dice.
6 ways to roll 5OAK
150 ways to roll 4OAK
1,500 ways to roll 3OAK (includes full houses)

Pot is $X

6 * 0.85 * X + 150 * 100 + 1,500 * Y - (7,776 - 1,500 - 150 - 6) = 0

Y is recursive EV of playing the game again. Will calculate when back in front of Excel.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
unJon
unJon
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camapl
August 4th, 2022 at 8:26:18 PM permalink
I take it back. The game doesnít make sense. You roll four of a kind just under 2% of the time. So you get paid 100:1 on a 50:1 shot? It would be +EV from the get go and the progressive shouldnít build, it should drain from the 4OAKs.

What am
I missing?
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.

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